David A Green,
Teletraffic Research Centre,
Department of Applied Mathematics,
University of Adelaide,
5005, Australia.
It is important to analyse the departure process of a queue, as it may be the arrival process to another queue in a network. In this paper we consider departure processes for MAP/PH/1 queues It appears that there cannot be a finite MAP description for the output process of a stationary MAP/PH/1 queue, in which the MAP is not a Poisson process. In an earlier paper, the author proposed and demonstrated the accuracy of a family of MAP approximations to the departure process of such queues. The structure of the defining processes is exploited in the approximations. An important feature of this family of approximations is that the kth approximation captures the first k-1 lag-correlation coefficients of the departure process exactly. In this paper we give a description of this family of approximations and a proof of the exactness of the correlation structure. By increasing the number of lag-correlation coefficients which are captured, the accuracy of the approximating process can also be increased. Some numerical examples of these approximations are given.